Pseudorelative Permeabilities for Simulation of Unstable Viscous Oil Displacement

Abstract

Summary Relative permeabilities are well understood for light oils involving stable displacement. However, conflicting arguments have been presented in the literature regarding relative permeabilities for viscous oils. Most nonthermal viscous oil displacements are unstable. Depending on the magnitude of mobility ratio, displacement is influenced by varying degrees of viscous instability, often referred to as fingering. For viscous oils (>500 cp), even a polymer flood must be designed at partially stable conditions (mobility ratio > 1) to maintain an economical processing rate [% pore volume (PV) injected (PVI) per year]. Typically, viscous fingering is difficult to model in full-field simulation because of the large grid sizes used. To design and optimize a partially stable polymer or waterflood, it is critical to correctly upscale the laboratory-generated relative-permeability curves for reservoir simulation. In recent years, such models have been published in the Society of Petroleum Engineers literature. Unfortunately, most of these models require multiple fitting parameters (at least three). In this work, we present a simplified technique that requires systematic change in only one parameter to generate upscaled relative permeability curve for a given viscosity ratio. Using fine-grid simulations, we show that the flow at high-viscosity ratio is channelized even in a core perceived to be homogeneous at laboratory scale. This happens because of small-scale heterogeneities that are present in every rock. Upscaling averages these fine variations in heterogeneities, causing the grids to be overswept, thus overpredicting recovery. To compensate for this shortcoming, it is recommended to upscale the relative-permeability curves in the simulation model.